The GPS system uses a constellation of satellites which rotate about the earth in very precisely determined orbits, that is to say the position of an arbitrary satellite can be ascertained at any instant. The orbits of the satellites are chosen in such a way that at any time, 6 to 12 satellites are visible at any point of the earth. Each satellite transmits two radioelectric signals of frequencies L1 (1575.42 MHz) and L2 (1227.6 MHz). On the ground or on a vehicle on land, sea or in the air, a GPS receiver receives the signals transmitted by visible satellites.
The onboard GPS receiver measures the duration of propagation required in order for a time mark transmitted by a satellite to reach it. The time marks are coded on carrier waves by the phase modulation technique. Each satellite thus transmits its own pseudo-random code. A replica of the sequence of the code is generated by the receiver and the shift that the replica must undergo so as to coincide with the code received corresponds to the duration of propagation of the signal in order to travel the satellite-receiver distance. This duration multiplied by the speed of light in the medium traversed gives a distance measurement called a pseudo-distance. On the basis of the measurements of the pseudo-distances separating it from each visible satellite, and of the knowledge of the position of the satellites, the receiver deduces its precise position in latitude, longitude, and in altitude in a terrestrial reference frame by a numerical resolution procedure akin to triangulation. It can also deduce therefrom the date and the precise time in the temporal reference frame of the GPS system.
The time reference of the receiver, provided by its clock, does not coincide perfectly with the time reference of the satellites of the constellation; this induces a bias in the measurements of propagation time, therefore of distance, that is equal to the delay of the time reference of the receiver with respect to the time reference of the satellites. The term “pseudo-distance” is employed for this purpose. The time bias, common to all the measurements, constitutes a fourth unknown, in addition to the three position unknowns, and this makes it necessary to have at least four measurements to calculate the position.
Furthermore, the position of the receiver is estimated by making a certain number of approximations. The measurement of the pseudo-distance cannot for example circumvent the system-related errors such as the lack of precision of the ephemerides or clocks onboard the satellites. The measurement of the pseudo-distance is also marred by errors related to the interactions between the signals and the atmospheric layers that they pass through. The signal propagation delay in the troposphere and the ionosphere is dependent on the inclination of the path and the time at which it takes place. Typically, GPS positioning errors related to the atmosphere are more marked by day than at night and more sensitive when a satellite is close to the horizon than the zenith. In certain applications such as for example a precision approach in aeronautics, the positioning precision obtained by a direct (or absolute) measurement of the pseudo-distance is not sufficient.
The use of a differential measurement makes it possible to substantially improve the precision of the positioning. It consists in transmitting, via a dedicated channel (VHF, UHF or cellular telephony), corrections of the pseudo-distance measurements formulated on the basis of pseudo-distance measurements originating from receivers disposed in ground stations and whose positions are very precisely known and close to the onboard receiver. The measurement of the pseudo-distance separating a ground receiver and a satellite is compared with the theoretical distance separating these two devices. The theoretical distance is calculated on the basis of the respective spatial coordinates of the ground receiver and of the satellite which are known at any instant. The difference between the distance measurement and the theoretical distance represents the measurement error, it is calculated for each satellite at each observation epoch. These distance differences constitute corrective terms (also called differential corrections) which are deducted from the pseudo-distance measurements carried out by the mobile receiver. These corrections have the effect of almost totally removing the errors which exhibit a significant spatial correlation whatever their origin, “system” or “atmospheric”. The corrections are all the more effective the closer the two receivers. However, the differential measurement does not eliminate the errors related to the reflections of the signal on objects that are close to the antenna of the receiver, nor the errors specific to the receiver (thermal noise). These errors are present in the reference receiver as well as in the onboard receiver, they degrade the positioning measurement during differential correction; the precision obtained is of the order of a few meters.
To improve the positioning precision, the ground receivers and carrier-borne mobile receivers, can also exploit a second cue formulated by the receiver which is the measurement of the phase of the carrier, for each satellite signal received. The measurement of the instantaneous phase of the carrier received actually makes it possible to calculate a pseudo-distance, termed the carrier pseudo-distance, between the receiver and the satellite, in the same way as the measurement of the instantaneous phase of the pseudo-random code. This carrier pseudo-distance undergoes the same variations as the code pseudo-distance, when the distance between the receiver and the satellite or the time bias due to the clock of the receiver vary. This pseudo-distance measured by the phase is a priori ambiguous since the phase is known modulo 2π but it is much less noisy than the code pseudo-distance measurements.
A known solution for improving pseudo-distance measurements consists in smoothing the noisy pseudo-distance measurement carried out on the code by the not very noisy phase measurements. For this purpose the receiver applies a low-pass filter to the difference between the code pseudo-distance and carrier pseudo-distance measurements, then adds this filtered difference to the carrier pseudo-distance measurement so as to reconstitute the code phase measurement. This processing is carried out satellite axis by satellite axis. If the measurement is differential, an identical smoothing is applied to the receivers of the ground station so that the tracking error of the low-pass filter, due to the divergence between the code and the carrier related to the fluctuations in the ionospheric delay, is identical on the ground and in the mobile receiver, and does not disturb the positioning measurement after application of the correction.
This solution represents the state of the art of the architecture of satellite navigation systems. Its main benefit lies in its simplicity and in the absence of any coupling effect between the measurements of the pseudo-distances of the various satellites (channels), nevertheless it is not completely satisfactory. Specifically, the gain in measurement precision is significant only when the smoothing is performed with a long time constant; and in this case, the duration of reinitialization to recover precision after an abrupt modification of all the available measurements (for example disappearance of a satellite by masking, failure of a satellite or else failure of a ground receiver in the case of differential GPS) is also long. It would be desirable to avoid this drawback.
Moreover, to quantify the integrity of the position measurement in applications where integrity is critical, such as aeronautical applications, a parameter called the position measurement “protection radius” is used. The protection radius corresponds to a maximum position error for a given probability of an error occurring. That is to say, the probability that the position error exceeds the stipulated protection radius is less than this given probability value. The calculation is based on two types of error which are on the one hand normal measurement errors and on the other hand errors caused by an operating anomaly in the constellation of satellites, by a failure of a satellite or else a failure of a ground receiver.
Commonly, two feared types of event that may arise with a GPS positioning system may be distinguished: the first, dubbed non-continuity, corresponds to an unplanned but declared degradation in the service; the second, called non-integrity, corresponds to an erroneous but undeclared position measurement, whose appearance is that of a reliable measurement. A non-continuity can correspond for example to the occurrence of an alarm indicating the supposed presence of a failure. In both cases the consequences can be serious, hence the necessity to minimize the probability of such events. A protection radius calculation can be estimated for a non-continuity probability value and a non-integrity probability value that are given a priori. In this case the probability that the positioning error exceeds the radius will be less than the given non-integrity probability, and the probability of alarm (justified or unjustified) will be less than the given non-continuity probability.
For example, in the case of existing systems which are based on smoothing, axis by axis, the pseudo-random code position measurements by the phase variations of the carrier, the protection radius degrades abruptly as a satellite disappears and takes a long time to regain an acceptable value after the satellite reappears, because of the response time of the smoothing filter. It would be desirable to find a solution which avoids this drawback. The invention is aimed in particular at minimizing this deterioration.